Question: How many numbers between $1$ and $100$ (inclusive) are divisible by $4$ or $9$ ?
Solution: There are $25$ numbers divisible by $4$ between $1$ and $100$, and $11$ numbers divisible by $9$ between $1$ and $100$. So, you might think there are $25 + 11 = 36$ numbers divisible by one or the other, but this is overcounting something. We're counting every number which is divisible by both $4$ and $9$ twice. So, for example, $36$ is counted once as a number divisible by $4$, and then again as a number divisible by $9$. So, we need to count how many numbers are divisible by both $4$ and $9$ and subtract this from what we had before. Being divisible by both $4$ and $9$ is the same thing as being divisible by $36$, so there are $2$ numbers between $1$ and $100$ divisible by both. Subtracting, there are $36 - 2 = 34$ numbers divisible by $4$ or $9$.